Non-separable Transform Research Articles

Efficient Dedicated Hardware Design System for the VVC Low-Frequency Non-Separable Transform

This paper proposes a dedicated hardware architecture for the Low-Frequency Non-Separable Transform (LFNST) of the Versatile Video Coding (H.266/VVC) standard. The VVC defines two stages of transformation, where the first stage uses traditional transform types (e.g. DCT-II, DCT-VII and DST-VII), while the secondary transform stage applies the LFNST. The LFNST is used to transform the coefficients that were transformed by the DCT-II in the primary transform, but only those from the residues that came from the intra prediction. The developed LFNST system design exploits the Clock Crossing Domain technique to extract the best relation between performance and area/power. Consequently, the design operates with two clock domains, where the core operates at a four times higher frequency than the primary transform. The ASIC synthesis results for a TSMC 40nm standard-cells library indicate that our design can process UHD 4K videos at 120 frames per second while using an area of 69.68 Kgates, and with a power dissipation of 40.46 mW. When compared with related works, our design presented the lowest power dissipation and energy consumption per sample.

Identification and Estimation of Nonseparable Transformation Models With Cross-sectional and Panel Data

Identification and Estimation of Nonseparable Transformation Models With Cross-sectional and Panel Data

Lightweight Hardware Transform Design for the Versatile Video Coding 4K ASIC Decoders

Versatile Video Coding (VVC) is the next generation video coding standard finalized in July 2020. VVC introduces new coding tools enhancing the coding efficiency compared to its predecessor High Efficiency Video Coding (HEVC). These new tools have a significant impact on the VVC software decoder complexity estimated to 2 times HEVC decoder complexity. In particular, the transform module includes in VVC separable and non-separable transforms named Multiple Transform Selection (MTS) and Low Frequency Non-Separable Transform (LFNST) tools, respectively. In this paper, we present an area-efficient hardware architecture of the inverse transform module for a VVC decoder. The proposed design uses a total of 64 regular multipliers in a pipelined architecture targeting Application-Specific Integrated Circuit (ASIC) platforms. It consists in a multi-standard architecture that supports the transform modules of recent MPEG standards including Advanced Video Coding (AVC), HEVC and VVC. The architecture leverages all primary and secondary transforms’ optimisations including butterfly decomposition, coefficients zeroing and the inherent linear relationship between the transforms. The synthesized results show that the proposed method sustains a constant throughput of 1 sample per cycle and a constant latency for all block sizes. The proposed hardware inverse transform module operates at 600 MHz frequency enabling to decode in real-time 4K video at 30 frames per second in 4:2:2 chroma sub-sampling format. The proposed module has been integrated in an ASIC UHD decoder targeting energy-aware decoding of VVC videos on consumer devices.

Testing conditional moment restriction models using empirical likelihood

Summary An empirical likelihood test is proposed for parameters of models defined by conditional moment restrictions, such as models with nonlinear endogenous covariates, with and without heteroscedastic errors and non-separable transformation models. The number of empirical likelihood constraints is given by the size of the parameter, unlike alternative semi-parametric approaches. We show that the empirical likelihood ratio test is asymptotically pivotal, without explicit studentization. A simulation study shows that the observed size is close to the nominal level, unlike alternative empirical likelihood approaches. It also offers a major advantage over two-stage least-squares, because the relationship between endogenous and instrumental variables does not need to be known. An empirical likelihood model specification test is also proposed.

Joint Separable and Non-Separable Transforms for Next-Generation Video Coding.

Throughout the past few decades, the separable Discrete Cosine Transform (DCT), particularly the DCT type II, has been widely used in image and video compression. It is well known that, under first-order stationary Markov conditions, DCT is an efficient approximation of the optimal Karhunen-Loève transform. However, for natural image and video sources, the adaptivity of a single separable transform with fixed core is rather limited for the highly dynamic image statistics, e.g., textures and arbitrarily directed edges. It is also known that non-separable transforms can achieve better compression efficiency for images with directional texture patterns, yet they are computationally complex, especially when the transform size is large. In order to achieve higher transform coding gains with relatively low-complexity implementations, we propose a joint separable and non-separable transform. The proposed separable primary transform, named Enhanced Multiple Transform (EMT), applies multiple transform cores from a pre-defined subset of sinusoidal transforms, and the transform selection is signaled in a joint block level manner. Moreover, a Non-Separable Secondary Transform (NSST) method is proposed to operate in conjunction with EMT. Unlike the existing non-separable transform schemes which require excessive amounts of memory and computation, the proposed NSST efficiently improves coding gain with much lower complexity. Extensive experimental results show that the proposed methods, in a state-of-the-art video codec, such as HEVC, can provide significant coding gains (average 6.9% and 4.5% bitrate reductions for intra and random-access coding, respectively).

A Theoretical Model of Optimal Forest Resource Regimes in Developing Economies

The standard economic theory of natural-resource management has its roots in a conventional economic theory of commons that overlooked the role of institutional structures and the transaction costs. Hence, it has not been able to explain cases of successful management of forests as common property. An economic model in-corporating the role of transaction costs has been developed. A mathematical form that can represent the general nature of a transaction function is suggested. Static models for separable and nonseparable transformation and transaction functions are discussed. The possibility of different resource regimes being optimal in different socioeconomic conditions is highlighted.